There are two basic prior art methods which have been applied to the investigation of sonar array performance. These may be classed as a theoretical/math modeling approach or as an experimental approach.
Despite the interest in sonar performance, mathematical modeling of arrays has developed slowly. Due to the complexities of element interactions, as well as interstitial and baffle effects, useful models have been restricted to a few simple geometries and, usually, to steady-state analyses. While some techniques have been applied to the transient case, they have required a priori knowledge of the velocity distributions in the array.
These prior art methods are described by (1) Stephanishen, P. R., "Transient Radiation from Pistons in an Infinite Planar Baffle", JASA, Vol 49, No. 5 (Part 2), 1971; and (2) Stepanishen, P. R., "An Approach to Computing Time-Dependent Interaction Forces and Mutual Radiation Impedances between Pistons in a Rigid Planar Baffle," JASA, Vol. 49, No. 1 (Part 2, 1971).
The simplifying assumptions, as well as incomplete knowledge of the operational environment of specific arrays, are basic limitations and often lead to large discrepancies between model predictions and actual array performance. An additional limitation is the large amount of computer memory and run time necessary to implement detailed models.
Three experimental methods have been applied to measurements of array parameters. These methods may be categorized as:
(1) interferometric methods, including holography; PA1 (2) accelerometer methods; and PA1 (3) acoustic loading methods.
The first, interferometric, method is capable of detecting displacements down to half the wavelength of the radiation used (light or sound). Interferometry or real-time stroboscopic holography can measure the magnitude of this displacement, though standard double-pulse holography does not record this information. A common problem, however, is that the actual displacements may be less than can be easily resolved for the case of a radiation-loaded transducer.
The second method employs accelerometers mounted directly to the radiating face of each array element. While the sensitivity of the accelerometer is high, its bandwidth is insufficient for doing transient studies. It is generally recommended that the resonant frequency of the accelerometor be at least five times that of the frequency of interest. This method is described by the ENDEVCO Corp. in their Instruction Manual, entitled "Piezoelectric Accelerometers".
Additionally, the metal encased accelerometers are sufficiently heavy to cause a noticeable parameter shift in the transducer and may be a significant portion of a wavelength in size at sonar frequencies. It is, furthermore, impractical to include such devices as a permanent part of the array.
The third, acoustic loading, technique employs a complementary array which, when electrically terminated in the proper manner, can be used as a dynamic mechanical load for the array under test. When thus properly loaded, an array may be driven to high power and its electrical parameters measured. As the complementary array has bandwidth capabilities similar to the first array, the technique cannot be applied for transient measurements, and may only be used if the array is planar.